Physics Chapter 3: 1-4: Vectors

Homework

Reading Preparation
Key Equations
WebLecture
Study Activity
Chat Preparation Activities
Chapter Quiz
Lab Work

Reading Preparation

Text Reading: Giancoli, Physics - Principles with Applications, Chapter 3: Sections 1-4

Study Points

Section 1: To work with quantities like displacement, velocity, and acceleration that have both a size or magnitude (scalar value) and a direction, we need to use vectors.
Section 2: Because vectors have direction as well as length, we have to take into account how the directions of vectors are related when we combine them. We can add vectors graphically, by putting the tail of each subsequent vector at the tip of the preceding vector, drawing a result vector from the tail of our first vector to the tip of our last vector.
Section 3: We subtract vectors graphically by reversing the direction of our second vector (the vector being subtracted). Multiplying vectors by scalars is really just scaling the vector; we don't change its direction.
Section 4: To work with vectors mathematically, we have to add, subtract, or multiply the sections of the vectors that lie in a common direction. To do this, we break vectors down into components that match the directions in our frame of reference (usually an x-y coordinate system). The actual vector is assumed to be the result of adding an x-direction and y-direction vector together.

Key Equations

Resultant Vector Displacement (Vector Form from Component Vectors)

\vec{D_{R}} = \vec{D_{x}} + \vec{D_{y}}

Resultant Vector Magnitude from Component Vectors

D_{R} = \sqrt{{D_{x}}^{2} + {D_{y}}^{2}}

Resultant Vector Direction from Component Vectors (θ measured counter-clockewise from x-coordinate.) $tan θ = \frac{D_{y}}{D_{x}}$

Web Lecture

Read the following weblecture before chat: Kinematics in Two and Three Dimensions

Study Activity

The Simulation below should run in your browser without an issue.

The "vector addition" applet lets you play with different representations of vectors in one or two dimensions Grab a vector arrow from the bucket, and drag it onto the graph area to experiment. The display bar will show you the magnitude of the resultant vector |R|, the angle with respect to the X axis θ (in 2D), and the component vectors R_x and R_y.

Place a vector with its tail at the origin, the manipulate the point of a very short vector (|R| < 5) to achieve angles of 45°, 135°, 225°, and 315°. What happens to the values of R_x and R_y? Are they always positive?
Place two vectors so that the tail of vector one is at the origin, and the tip is at the tail of vector two. Click the "Show Sum" option and move the resultant vector so that its tail rests on the tail of vector one. What happens now as you move the tip of vector two?
Use the Style options to display the X and Y components of the vectors in different combinations.
Try to solve one of the vector addition homework problems in your text using the simulation.

Physics simulations are the product of the PHET Interactive Simulations project at the University of Colorado, Boulder.

Chat Preparation Activities

Forum question: The Moodle forum for the session will assign a specific study question for you to prepare for chat. You need to read this question and post your answer before chat starts for this session.
Mastery Exercise: The Moodle Mastery exercise for the chapter will contain sections related to our chat topic. Try to complete these before the chat starts, so that you can ask questions.

Chapter Quiz

The chapter quiz is not yet due.

Lab Work

If you want lab credit for this course, you must complete at least 18 labs; you may complete more if you are preparing for the AP exam.. One or more lab exercises are posted for each chapter as part of the homework assignment. We will be reviewing lab work at regular intervals, so do not get behind!

Lab Instructions: Projectiles

© 2005 - 2025 This course is offered through Scholars Online, a non-profit organization supporting classical Christian education through online courses. Permission to copy course content (lessons and labs) for personal study is granted to students currently or formerly enrolled in the course through Scholars Online. Reproduction for any other purpose, without the express written consent of the author, is prohibited.

Physics

Chapter 3:1-4 Assignment